# apaseq

Pseudorandom binary maximum length sequence

Since R2024a

## Syntax

``S = apaseq(N)``

## Description

example

````S = apaseq(N)` generates a length-N pseudorandom binary almost-perfect autocorrelation sequence (APAS) `S`. An APAS sequences has a periodic autocorrelation function (PACF) that is zero for all nonzero lags except at N/2.```

## Examples

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Create a phase modulated continuous wave (PMCW) waveform based on an almost perfect autocorrelation sequence (APAS) of length N = 64. Assume the chip width is tau = 1e-6 s. Plot the periodic ambiguity function to verify that it has zero sidelobe level everywhere except at tau*N/2.

Create an APAS of length N.

```N = 64; s = apaseq(N);```

Set the chip width and modulation period.

```tau = 1e-6; T = tau*N; fs = 10/tau;```

Create a custom phase coded waveform System object™ and generate waveform samples. Set PRF to be equal to the inverse of the modulation period.

```waveform = phased.PhaseCodedWaveform(SampleRate=fs,Code="Custom", ... CustomCode=s,ChipWidth=tau,PRF=1/T); x = waveform();```

Plot the periodic ambiguity function to verify that it has zero sidelobes everywhere except at tau*N/2.

`pambgfun(x,fs,1/T,Cut="Doppler");`

## Input Arguments

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Code sequence length, specified as integer such that N=2*(p+1), where p is a prime number.

Example: `28`

Data Types: `double`

## Output Arguments

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Code sequence, returned as a length-N complex-valued column vector. The returned sequence is antipodal, that is it consists of only 1 and -1. The height of the PACF sidelobe at N/2 is N-4.

Data Types: `double`
Complex Number Support: Yes

## Algorithms

The `apaseq` function uses an algorithm described in [1] to generate an APAS sequence from a p-ary m-sequence D of length M=p2-1. At first, all elements of the APAS S are initialized to -1. Then, the indices of the elements in S that must be set to 1 are obtained as mod(I-1,N)+1, where % I contains indices of the elements in D that are equal to 1.

## References

[1] Pott, Alexander, and Steven P. Bradley. "Existence and nonexistence of almost-perfect autocorrelation sequences." IEEE transactions on information theory 41, no. 1 (1995): 301-304.

[2] Haderer, Heinz, Reinhard Feger, and Andreas Stelzer. "A comparison of phase-coded CW radar modulation schemes for integrated radar sensors." In 2014 44th European Microwave Conference, pp. 1896-1899. IEEE, 2014.

[3] Levanon, N. and E. Mozeson. Radar Signals. Hoboken, NJ: John Wiley & Sons, 2004.

## Version History

Introduced in R2024a